Philosophical, Logical, and Experimental routes to substructurality

Project Information

PLEXUS

Grant agreement ID: 101086295

DOI

10.3030/101086295

EC signature date 18 October 2022

Start date 1 January 2023

End date 31 December 2026

Funded under

• Marie Skłodowska-Curie Actions (MSCA)

Total cost

No data

EU contribution

€ 556 600,00

Coordinated by

UNIVERSIDAD DE NAVARRA
Spain

Periodic Reporting for period 1 - PLEXUS (Philosophical, Logical, and Experimental routes to substructurality)

Reporting period: 2023-01-01 to 2024-12-31

Summary of the context and overall objectives of the project

OBJECTIVES

Classical Logic (the logic devised by Frege at the birth of modern mathematical logic) provides a sharp characterisation of our reasoning in abstract fields like mathematics. However, Classical Logic seems to be inadequate in relation to several phenomena such as vagueness, conditionals or paradoxes. Substructural logics – logics where some structural rule, like weakening, contraction or exchange, can fail – are alternatives to Classical Logic that have attracted a lot of attention by logicians in the last decade. The EU-funded PLEXUS project will study these logics with particular emphasis on "radically substructural logics" – non-transitive and non-reflexive logics. Specifically, PLEXUS will investigate the main philosophical challenges raised by radically substructural logics, their proof-theoretic and model theoretic characterisations and their logico-linguistic applications.

The overall goal of PLEXUS is articulated into three main research objectives:

Objective 1. Philosophical Foundations: PLEXUS will investigate the major philosophical challenges raised by non-transitive and non-reflexive substructural logics.

Objective 2. Logic: PLEXUS will advance knowledge of the field of substructural logics by developing new proof-theoretic and model-theoretic characterizations of radically substructural logics.

Objective 3. The Metainferences Inventory & Metainferences Prover: PLEXUS seeks to design and validate a psychometric tool (i.e. the Metainferences Inventory) which would allow us to measure naïve speakers' preferences on different questions about radical substructurality. Complementary to this research, PLEXUS will extend existing techniques of automated reasoning to the logics covered by the project, focusing particularly on the decision of validity for metainferences.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

Objective 1. Philosophical Foundations. Progress on radical substructural logics ST and TS by the study of their characterization in terms of natural set theoretic operations and by the study of lattices formed by many-valued logics. We also made progress on the conceptualization of substructurality and the availability of formal methods to show how classical reasoning can be retained in a substructural setting (classical recapture). In connection to this objective, we also extended the analysis of radical substructurality to alternative contexts (intuitionistic logic, weak Kleene logics, four-valued semantics, probabilistic consequence relations).

The work-package related to this objective involves a significant number of researchers (9 ER and 4 ESR) and secondments (39 months of secondments planned). The implementation of these was fruitful in collaborations between experienced and early stage researchers. All the scientific events up to date (inaugural conference, workshop, intensive courses, summer school) relate to this scientific objective. In addition to these, we organized 10 extra events of networking and knowledge sharing that were not planned in the original proposal.

Objective 2. Logic. In relation to this objective, we advanced knowledge of the technical aspects of radical substructural logics, focusing primarily on the development of different sort of calculus (sequents, labelled sequents, natural deduction) and model theoretic and algebraic approximations to radical substructural logics. We also conducted research on the applications of substructural logics to different domains like: self-applicable truth, conditionals and epistemic phenomena.

The work-package related to objective 2 is the largest with 50 months of secondments (+14 months in KCL) and 23 researchers (9 ESR and 14 ER). The secondments, from EU institutions to either CUNY or CONICET were extremely fruitful and lead to collaborations between experienced researchers and younger scholars in the form of paper writing and, also, some co-supervisions. All of PLEXUS’ scientific events had an impact on WP2 and, as we mentioned in relation to objective 1, during this period more scientific events were implemented within the PLEXUS network than originally planned.

Objective 3. The Metainferences Inventory & Metainferences Prover. The progress of the work-package related to objective 3 concerns (i) the conceptualization, design, debriefing and pretesting of the Inventory and (ii) the analysis of theorem provers and the first steps towards the construction of a theorem prover for metainferences. Regarding (i) the team in Navarra prepared a first draft of the Inventory with two pilot tests. Regarding (ii) the team in CONICET advanced on the accommodation of the Python package Logics to trees for metainferences for Strong Kleene Logics as well as with the adaptation of the web interface Taut. Two PhD students in Navarra were trained and took the first steps towards the construction of a tree proof generator for metainferences for Strong Kleene Logics.

There were five secondments in this period in the work-package for objective 3 involving two ESRs and two ERs. One of the Intensive Courses was dedicated to knowledge sharing of experimental methods (Behavioural Logic & Principles of Assessing Behaviour). The Workshop on Logic and Reasoning held in Buenos Aires in November 2024 was dedicated to this WP. One of the courses of the Summer School explained the fundamentals of automated reasoning in ProLog.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

As a project of theoretical nature, the main results of it materialized in the form of scientific publications, the intensity of knowledge transfer and collaborations, the PhD supervision and the synergetic relations with other research groups.

39 works were published. These publications can be reviewed in the PLEXUS community in Zenodo: https://zenodo.org/communities/id101086295/

Intensity of knowledge transfer and scientific collaboration: 7 events plus 10 extra (not planned in the original proposal); papers co-authored by two or more PLEXUS members: 13 out of 28 scientific articles.

The action involves around 20 early stage researchers and 25 experienced researchers. 3 PhD thesis were completed during the first period. The secondments propitiated the collaboration of PhD supervision between PLEXUS members: several early stage researchers work now under the co-supervision of some PLEXUS experienced researcher from an institution different from the one she/he is doing its PhD.


Societal Impact

PLEXUS seeks to enhance the visibility of the scientific activity in Europe, attracting talented young scholars to the study of philosophical and logical problems, and instilling a culture of research, innovation, tolerance, and diversity. We further worked to increase the visibility of women in the scientific landscape of Europe.

We worked on the visibility of scientific activity in Europe by broadcasting all PLEXUS events, publishing talks and seminars in the PLEXUS YouTube channel and, more generally, through the PLEXUS communication and dissemination activities.

In relation to the visibility of the work of women in Logic and Philosophy, all the PLEXUS events counted with a significant number of female researchers (keynotes speakers in the Inaugural Conference, in the Workshop and Summer School). Of the 15 ESR that already did a secondment or have a planned secondment for 2025, we find 9 male and 6 female persons. The event Women in PLEXUS was organized by four female ESR of PLEXUS and gathered several researchers among with women and other underrepresented groups.

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